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[5 marks] The network on the right shows a convolutional layer in a larger network. The input is e R50. Consider the kernel (or filter)
[5 marks] The network on the right shows a convolutional layer in a larger network. The input is e R50. Consider the kernel (or "filter") A, with 9 elements and a bias, so that the input current for the next layer is Zj = b + A; ;ti-1 for j = 1, ..., 42. i=1 where b is the kernel's bias. Then hj = o(2) for some activation function o.). Suppose you are given the gradient of the loss function with respect to these input currents, E., j = 1, ..., 42. Write a formula that computes the derivative of the loss function with respect to the ith element of the convolution kernel. That is, write a formula to compute E, for i = 1, ...,9. 1 [5 marks] The network on the right shows a convolutional layer in a larger network. The input is e R50. Consider the kernel (or "filter") A, with 9 elements and a bias, so that the input current for the next layer is Zj = b + A; ;ti-1 for j = 1, ..., 42. i=1 where b is the kernel's bias. Then hj = o(2) for some activation function o.). Suppose you are given the gradient of the loss function with respect to these input currents, E., j = 1, ..., 42. Write a formula that computes the derivative of the loss function with respect to the ith element of the convolution kernel. That is, write a formula to compute E, for i = 1, ...,9. 1
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